It's time for me to update my camera, as my TZ1 now struggles to focus, (I'm a amateur). I'd like a compact all round camera: low light, outdoors, landscapes, people etc and am keen to develop my photography skills. My friend has a LX5 and I love the light and look of the photos and how compact the camera is. Downsides for me are not full HD function and lack of zoom. The G3 seems to be the next option to overcome these issues, but I see there are no similar lens and it looks like the mirrorless ILC market is developing quickly so maybe I should wait and see what else comes along, (any brand)? Looking for a camera I will have for a long time.

The lens is bright on the LX5, but the sensor is MUCH bigger on an ILC. Depends which is more important to you. I'd sacrifice some of the zoom range and get an ILC myself. Unless you want something really small, in which case get a Canon S95 / S100.

It depends a lot on what you are after. Compact size? Performance? Try to figure out where your balance is.

Even though I own a semi-pro DSLR, I still feel I am learning all the time. That is why I wanted a second camera I could have on me most of the time. Something that allows me to get more shots, more practice. After looking at all the option available, I ended up with the Canon S95. It's (relatively) cheap, very compact, and delivers decent image quality. I realized that as much as I love image quality, I would benefit more from a compact size. Plus, I still have the DSLR for serious work.

A compact like the LX5 is great to have with you on a regular basis and it can still produce the quality required for prints. That could help develop your skills. If, however, you don't much feel like having a camera on you all the time and don't mind a bit more bulk when you do bring the camera along, a G3 or GX1 will be capable of higher quality images. The GX1 with new pancake zoom is even quite small and because they have interchangeable lenses it is easy to find a lens for every occasion.

I do agree that there is too much movement in the ILC market. One of my main reasons for not buying one. I will use the S95 for now and see what happens.
As for Canon, the new S100 does have 1080p HD video and a bit more zoom.